Abstract
In this paper we give an outlook on the problem pertinent to the structural stability of hydrated double-stranded (duplex) M +1 -DNA salts (M +1 stands for a monovalent counterion like Na+, K+, Rb+) in fibers and possibly in solutions. In particular we call attention to the processes which may occur at the interface between the polyion and its aqueous surroundings and to their relations with external control parameters like water activity aw and ionic strength I.
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References
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The shell-mode coupling involving asymmetric stretching and symmetric bending certainly affects the P-01, P-02 double-bond character, but it is expected not to affect directly the backbone conformation as far as the negative charge delocalization concerns only the two “pendent” oxygens. If, however, such delocalization would involve ester oxygens, a change in dihedral angles α and ζ will then affect the resonance integrals in the π-like system of orbitals of the whole phosphate group, so that an (α,ζ)-dependent energy term would appear. Of course, the actual situation will depend on the strength and symmetry of the ligand fields (absorbed water molecules and possibly coordinated counterions). This state of affairs may be tentatively approached in terms of a mean field theory following the same method as in ferroelectrics. (See, for instance, M. Tokunaga, M. Matsubara: Progr. Theor. Phys. 35, 581 (1966)
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During the elaboration of the present analysis we became aware of the work of De Santis (see Ref. [10]) where the same type of argument is employed
In the rough approximation in which β is kept constant at “trans” (t) position (β~180°), Eq. (14) would also imply cosγ = 0, or cosγ = -1. The former solution may be ascribed to both g+ or g- ranges; if ascribed to g+, this result appears to be consistent with the experimental observation (see Sect.2). Furthermore, the constancy of both β and γ implying two more equations (contraints) among α,ε,ζ allows one to choose ζ as relevant conformational parameter. Of course, for fixed δ, the other parameters become functions of the free ζ.
It appears that the stability of the water spine in the m.g. depends on base sequence, it is then a problem which should be treated in the framework of DNA genetic-dependent properties (see the introductory section)
Alternatively, by remembering the strict relation existing between sugar puckering and pseudorotation, one may think of a situation in which the energy barrier for (C2′-endo)→(C3′-endo) transition of sugar is controlled by the fluctuations in phosphate-group rotation ζ and, vice versa, the energy barrier for (t)→(g+) transition of phosphate group rotation ζ is controlled by fluctuations in sugar pseudorotation. Such a situation should be formally similar to that of dynamic barriers occurring in proteins, as suggested by H. Frauenfelder: Biochemistry 23, 5147 (1980)
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Note that the relation of Eq. (25) with second-order differential entropy ‘(see, for instance: Nicolis and Prigogine, Ref. [4] is trivial: \( {({\delta^2}S)_0} \equiv - (1/T)\sum\limits_{{ij}} {{{({\partial^2}G/\partial {\xi_i}\partial {\xi_j})}_0}\partial {\xi_i}\partial {\xi_j}} \) where the subscript (0) denotes “reference state” and {∂ξj} stands for the order parameters ζ,σ,ξ,θA,θB1,θB2; further considerations on kinetic properties of fluctuations, namely terms involving ∇ξj(Z,r,φ;t), would lead us to the wanted relaxation equations, at least for regimes near to equilibrium
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Nardelli, G.F., Bracale, M., Signorini, C., Zucchelli, G. (1983). Stability of Hydrated M +1 -DNAs: A Challenge in the Theory of Nonlinear Systems. In: Benedek, G., Bilz, H., Zeyher, R. (eds) Statics and Dynamics of Nonlinear Systems. Springer Series in Solid-State Sciences, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82135-6_6
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DOI: https://doi.org/10.1007/978-3-642-82135-6_6
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